Principal Quantum number by size?

In summary, the value of the principal quantum number for a hydrogen atom to have a size of one micron is approximately 97. This number can theoretically go up to infinity, but in practice, an atom with such a high n would eventually lose its electron through collisions.
  • #1
physics(L)10
101
0

Homework Statement


What is the value of the principal quantum number for a hydrogen atom to have a size of one micron?

Homework Equations


r=(5.3x10-11)(n2)
r=1x10-6/2=5x10-7

The Attempt at a Solution



5x10-7=(5.3x10-11)(n2)

97.1 = n

How is this possible? lol Maybe it's more complicated then I'm thinking.
 
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  • #2
Just use the nearest integer value.
 
  • #3
So I'm right? The answer is just 97? I thought the principal quantum numbers (n) only go up to like 5 or 6 or something like that though.
 
  • #4
Yes, you're right. n can go up to infinity in theory. In practice, an atom with such a high n would eventually collide with another atom or perhaps a container wall, and completely lose the electron.
 
  • #5
Alrighty, thank you very much :)
 

Related to Principal Quantum number by size?

What is the principal quantum number?

The principal quantum number, denoted by the letter n, is an integer that represents the energy level or shell of an electron in an atom.

How does the principal quantum number relate to the size of an atom?

The principal quantum number indirectly affects the size of an atom by determining the distance of the electron from the nucleus. As the value of n increases, the distance between the electron and the nucleus also increases, resulting in a larger atomic size.

What is the maximum value of the principal quantum number?

The maximum value of the principal quantum number is determined by the number of electrons in an atom. It can be calculated using the formula 2n², where n is the number of electron shells in an atom. For example, an atom with 3 electron shells can have a maximum n value of 3, resulting in a maximum of 18 electrons.

How does the principal quantum number affect the energy of an electron?

The principal quantum number is directly related to the energy of an electron. As the value of n increases, the energy level of the electron also increases. This means that electrons in higher energy levels have more energy than those in lower energy levels.

Can atoms have the same principal quantum number?

Yes, atoms can have the same principal quantum number. However, they will have different values for other quantum numbers, such as the azimuthal quantum number and magnetic quantum number, which determine the shape and orientation of the electron's orbit. This means that even with the same n value, the electrons in these atoms will have different energy levels and positions within the atom.

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